3750.21 – Negating Barbells

Suppose the statement: "All sets of barbells at Dicks Sporting Goods are on sale" is false. Then which of the following statements must be true?

I. All sets of barbells at Dicks are not on sale.

II. There is some set of barbells at Dicks that is not on sale.

III. No set of barbells at Dicks is on sale.

IV. Not all sets of barbells at Dicks are on sale.

  1. II

  2. IV

  3. I and III

  4. II and IV

  5. I, II, and IV

Solution

The answer is d: II and IV.